Getting your eyes in line with the ball early and trying to get your head over the ball doesn't get you into totally the wrong position, which is kind of the point.
On the contrary, an over-riding obsession with getting the head in line with the ball leads to the exact vulnerability to late inswing/inseam that OP describes. Its actually more likely that he is leading TOO STRONGLY with the head, and getting it outside the (post-deviation) line of the ball. Telling him to lead even more with his head is only going to make the problem worse.
The key to playing swing is to avoid overcommitting to playing a particular line, but instead using smaller movements to get into a more balanced adaptable position, where you can access the ball whether it moves in or away, and then trust in your hands to instinctively adjust to any late movement.
I've been coaching a group of teenagers this winter this exact thing using tennis balls half covered in tape and throwing them at them at 70mph with random swing directions. Teaching them to use small movements, stay relaxed, and trust their hands has improved their skills considerably - if I had said "lead with your head", they'd still be getting clean bowled every ball.